The access points can sometimes "bug out" on the airprint packets. The quickest way to recover is to reset the access points in the building (sometimes using technology manager to disable/enable will work as well). The church technology people have stated they do not officially support Airprint, so they will be of no hope for troubleshooting.
The Airprint bug only happens over wireless, if you plug a laptop into the ethernet network, the printers come right up regardless of wireless printing issues.
One tip. Make sure the "wireless" printer is physically plugged into the network (you may need to use a switch in the clerk's office). Stay away from wireless only printers (the cheaper consumer ones do not have ethernet ports).
Facilities will not install additional network jacks in clerks/Bishops offices by default (mileage may vary depending on your FM manager).
Android devices do not experience the airprint bug as they connect directly to the printers via printer apps (HP, Xerox, etc...). They will have a narrower support of printers though, as not all printers support the Manufacture's Printing App.